Sun, Min Merit functions and equivalent differentiable optimization problems for the extended general variational inequalities. (English) Zbl 1213.90233 Int. J. Pure Appl. Math. 63, No. 1, 39-49 (2010). Summary: We study some merit functions and equivalent differentiable optimization problems for the extended general variational inequalities involving three operators, which was introduced and studied by M. A. Noor [Projection iterative methods for extended general variational inequalities, J. Appl. Math. Comput. 32, No. 1, 83–95 (2009)] very recently. Using the projection technique, we obtain some error bounds for the solution of extended general variational inequalities under some mild conditions, and then formulate the extended general variational inequalities as differentiable constrained (or unconstrained) optimization problems. We also prove that the extended general variational inequalities have a unique solution under some conditions. Cited in 2 Documents MSC: 90C30 Nonlinear programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:error bounds PDFBibTeX XMLCite \textit{M. Sun}, Int. J. Pure Appl. Math. 63, No. 1, 39--49 (2010; Zbl 1213.90233)